aboutsummaryrefslogblamecommitdiffstats
path: root/lib/ic/src/iceval.erl
blob: 81093dcd5b3bb6d1c28bfde42a34b2199b56d35f (plain) (tree)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555









































































































































































































































































































































































































































































































































































                                                                                               
%%
%% %CopyrightBegin%
%% 
%% Copyright Ericsson AB 1997-2009. All Rights Reserved.
%% 
%% The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
%% compliance with the License. You should have received a copy of the
%% Erlang Public License along with this software. If not, it can be
%% retrieved online at http://www.erlang.org/.
%% 
%% Software distributed under the License is distributed on an "AS IS"
%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
%% the License for the specific language governing rights and limitations
%% under the License.
%% 
%% %CopyrightEnd%
%%
%%
-module(iceval).

-include("icforms.hrl").

-export([eval_const/5, eval_e/5]).

-export([check_tk/3, get_val/1, mk_val/1]).

-define(get_max(__X, __Y), if __X > __Y -> __X; true -> __Y end).
-define(get_min(__X, __Y), if __X > __Y -> __Y; true -> __X end).

-define(BASE, 100000000000000000000000000000000).
-define(FIXED_MAX, 9999999999999999999999999999999).

%% Called fr: ictype 99, 522, 533
%% Fixed constants can be declared as:
%% (1)  const fixed pi = 3.14D; or
%% (2)  typedef fixed<3,2> f32;
%%      const f32 pi = 3.14D;
%% Hence, if fixed is declared as (1) we must handle it especially.
eval_const(G, S, N, tk_fixed, Expr) ->
    case catch eval_e(G, S, N, tk_fixed, Expr) of
	T when element(1, T) == error -> 0;
	V when is_record(V, fixed) -> 
	    {ok, {tk_fixed, V#fixed.digits, V#fixed.scale}, V};
	V ->
	    ic_error:error(G, {bad_tk_match, Expr, tk_fixed, get_val(V)})		      
    end;
eval_const(G, S, N, TK, Expr) ->
    case catch eval_e(G, S, N, TK, Expr) of
	T when element(1, T) == error -> 0;
	V -> 
	    case check_tk(G, TK, V) of
		true -> ok;
		false ->
		    ic_error:error(G, {bad_tk_match, Expr, TK, get_val(V)})
	    end,
	    get_val(V)
    end.


check_op(G, S, N, Tk, Types, Op, E1, E2) ->
    V1 = eval_e(G, S, N, Tk, E1),
    V2 = eval_e(G, S, N, Tk, E2),
    check_types(G, Op, E1, Types, V1),
    check_types(G, Op, E2, Types, V2),
    case check_comb(V1, V2) of
	true ->
	    {V1, V2};
	false ->
	    Err = {bad_type_combination, E1, get_val(V1), get_val(V2)},
	    ic_error:error(G, Err),
	    throw({error, Err})
    end.

check_op(G, S, N, Tk, Types, Op, E1) ->
    V1 = eval_e(G, S, N, Tk, E1),
    check_types(G, Op, E1, Types, V1),
    V1.

%% Match the declared type TK against the factual value of an constant
%%
check_tk(_G, _Any, default) -> true;		% Default case in union
check_tk(_G, positive_int, V) when is_integer(V) andalso V >= 0 -> true;
check_tk(_G, tk_long, V) when is_integer(V) -> true;
check_tk(_G, tk_longlong, V) when is_integer(V) -> true;  %% LLON_G
check_tk(_G, tk_short, V) when is_integer(V) -> true;
check_tk(_G, tk_ushort, V) when is_integer(V) andalso V >= 0 -> true;
check_tk(_G, tk_ulong, V) when is_integer(V) andalso V >= 0 -> true;
check_tk(_G, tk_ulonglong, V) when is_integer(V) andalso V >= 0 -> true;  %% ULLON_G
check_tk(_G, tk_float, V) when is_float(V) -> true;
check_tk(_G, tk_double, V) when is_float(V) -> true;
check_tk(_G, tk_boolean, V) -> is_bool(V);
check_tk(_G, tk_char, {char, _V}) -> true;
check_tk(_G, tk_wchar, {wchar, _V}) -> true; %% WCHAR
check_tk(_G, {tk_string, _Len}, {string, _V}) -> true;
check_tk(_G, {tk_wstring, _Len}, {wstring, _V}) -> true;  %% WSTRING
check_tk(_G, {tk_fixed, Digits, Scale}, {fixed, Digits, Scale, _V}) -> true;
check_tk(_G, tk_octet, V) when is_integer(V) -> true;
%%check_tk(_G, tk_null, V) when integer(V) -> true;
%%check_tk(_G, tk_void, V) when integer(V) -> true;
%%check_tk(_G, tk_any, V) when integer(V) -> true;
%%check_tk(_G, {tk_objref, "", "Object"}, V) when integer(V) -> true.
check_tk(_G, {tk_enum, _, _, Body}, {enum_id, Id}) -> 
    until(fun(X) when X == Id -> true;
	     (_X) -> 
		  false 
	  end, Body);
check_tk(_G, _TK, _V) ->
    false.

get_val({string, X}) -> X;
get_val({wstring, X}) -> X;  %% WCHAR
get_val({char, X}) -> X;
get_val({wchar, X}) -> X;  %% WSTRING
get_val({enum_id, X}) -> X;
get_val(X) -> X.

check_types(G, Op, Expr, TypeList, V) ->
    case until(fun(int) when is_integer(V) -> true;
		  (float) when is_float(V) -> true;
		  (bool) when V==true -> true;
		  (bool) when V==false -> true;
		  (fixed) when is_record(V, fixed) -> true;
		  (_) -> false end,
	       TypeList) of
	true -> true;
	false ->
	    Err = {bad_type, Expr, Op, TypeList, V},
	    ic_error:error(G, Err),
	    throw({error, Err})
    end.

%%get_op(T) when tuple(T) -> element(1, T).

%% Should be in lists
until(F, [H|T]) ->
    case F(H) of
	true -> true;
	false -> until(F, T)
    end;
until(_F, []) -> false.

%% Section of all the boolean operators (because Erlang ops don't like
%% boolean values.
e_or(X, Y) when is_integer(X) andalso is_integer(Y) -> X bor Y;
e_or(true, _) -> true;
e_or(_, true) -> true;
e_or(_, _) -> false.

e_and(X, Y) when is_integer(X) andalso is_integer(Y) -> X band Y;
e_and(true, true) -> true;
e_and(_, _) -> false.

e_xor(X, Y) when is_integer(X) andalso is_integer(Y) -> X bxor Y;
e_xor(X, X) -> false;
e_xor(_, _) -> true.

%% Handling infix operators (+,-,*,/) for fixed type.
%% Boundries determined as fixed<max(d1-s1,d2-s2) + max(s1,s2) + 1, max(s1,s2)>
e_fixed_add(#fixed{digits = D1, scale = S1, value = V1}, 
	    #fixed{digits = D2, scale = S2, value = V2}) ->
    Scale = ?get_max(S1, S2),
    Digits = ?get_max((D1-S1), (D2-S2)) + Scale +1,
    %% We must normalize the values before adding. Why?
    %% 4.23 and 5.2 are represented as 423 and 52. To be able to get the 
    %% correct result we must add 4230 and 5200 == 9430.
    {PV1, PV2} = normalize(S1, V1, S2, V2),
    check_fixed_overflow(#fixed{digits = Digits, 
				scale = Scale, 
				value = (PV1 + PV2)}).

%% Boundries determined as fixed<max(d1-s1,d2-s2) + max(s1,s2) + 1, max(s1,s2)>
e_fixed_sub(#fixed{digits = D1, scale = S1, value = V1}, 
	    #fixed{digits = D2, scale = S2, value = V2}) ->
    Scale = ?get_max(S1, S2),
    Digits = ?get_max((D1-S1), (D2-S2)) + Scale +1,
    {PV1, PV2} = normalize(S1, V1, S2, V2),
    check_fixed_overflow(#fixed{digits = Digits, 
				scale = Scale, 
				value = (PV1 - PV2)}).

%% Boundries determined as fixed<d1+d2, s1+s2>
e_fixed_mul(#fixed{digits = D1, scale = S1, value = V1}, 
	    #fixed{digits = D2, scale = S2, value = V2}) ->
    check_fixed_overflow(#fixed{digits = (D1+D2), 
				scale = (S1+S2), 
				value = V1*V2}).

%% Boundries determined as fixed<(d1-s1+s2) + s inf ,s inf>
e_fixed_div(#fixed{digits = D1, scale = S1, value = V1}, 
	    #fixed{digits = _D2, scale = S2, value = V2}) ->
    {PV1, PV2} = normalize(S1, V1, S2, V2),
    DigitsMin = (D1-S1+S2),
    R1 = (PV1 div PV2),
    R2 = (R1*?BASE + (PV1 rem PV2) * (?BASE div PV2)),
    {Result2, Sinf} = delete_zeros_value(R2, 0, R1),
    check_fixed_overflow(#fixed{digits = DigitsMin + Sinf, scale = Sinf, 
				value = Result2}).


%% Checks combination of argument types, basically floats and ints are
%% interchangeable, and all types are allowed with themselves. No
%% other combinations are allowed
%%
check_comb(X, Y) when is_integer(X) andalso is_integer(Y) -> true;
check_comb(X, Y) when is_float(X) andalso is_integer(Y) -> true;
check_comb(X, Y) when is_integer(X) andalso is_float(Y) -> true;
check_comb(X, Y) when is_float(X) andalso is_float(Y) -> true;
check_comb({X, _}, {X, _}) -> true;		% Strings and chars are tuples
check_comb({fixed, _, _, _}, {fixed, _, _, _}) -> true;
check_comb(X, Y) ->
    case {is_bool(X), is_bool(Y)} of
	{true, true} -> 
	    true;
	_ -> 
	    false
    end.

is_bool(true) -> true;
is_bool(false) -> true;
is_bool(_) -> false.


%%%% (15)
eval_e(G, S, N, Tk, {'or', T1, T2}) ->
    {E1, E2} = check_op(G, S, N, Tk, [int, bool], 'or', T1, T2),
    e_or(E1, E2);

%%%% (16)
eval_e(G, S, N, Tk, {'xor', T1, T2}) ->
    {E1, E2} = check_op(G, S, N, Tk, [int, bool], 'xor', T1, T2),
    e_xor(E1, E2);

%%%% (17)
eval_e(G, S, N, Tk, {'and', T1, T2}) ->
    {E1, E2} = check_op(G, S, N, Tk, [int, bool], 'and', T1, T2),
    e_and(E1, E2);

%%%% (18)
eval_e(G, S, N, Tk, {'rshift', T1, T2}) ->
    {E1, E2} = check_op(G, S, N, Tk,  [int], 'rshift', T1, T2),
    E1 bsr E2;
eval_e(G, S, N, Tk, {'lshift', T1, T2}) ->
    {E1, E2} = check_op(G, S, N, Tk, [int], 'lshift', T1, T2),
    E1 bsl E2;

%%%% (19)
eval_e(G, S, N, Tk, {'+', T1, T2}) ->
    case check_op(G, S, N, Tk, [int, float, fixed], '+', T1, T2) of
	{F1, F2} when is_record(F1,fixed) andalso is_record(F2,fixed) ->
	    e_fixed_add(F1, F2);
	{E1, E2} ->
	    E1 + E2
    end;
eval_e(G, S, N, Tk, {'-', T1, T2}) ->
    case check_op(G, S, N, Tk, [int, float, fixed], '-', T1, T2) of
	{F1, F2} when is_record(F1,fixed) andalso is_record(F2,fixed) ->
	    e_fixed_sub(F1, F2);
	{E1, E2} ->
	    E1 - E2
    end;

%%%% (20)
eval_e(G, S, N, Tk, {'*', T1, T2}) ->
    case check_op(G, S, N, Tk, [int, float, fixed], '*', T1, T2) of
	{F1, F2} when is_record(F1,fixed) andalso is_record(F2,fixed) ->
	    e_fixed_mul(F1, F2);
	{E1, E2} ->
	    E1 * E2
    end;
eval_e(G, S, N, Tk, {'/', T1, T2}) ->
    case check_op(G, S, N, Tk, [int, float, fixed], '/', T1, T2) of
	{F1, F2} when is_record(F1,fixed) andalso is_record(F2,fixed) ->
	    e_fixed_div(F1, F2);
	{E1, E2} ->
	    E1 / E2
    end;
eval_e(G, S, N, Tk, {'%', T1, T2}) ->
    {E1, E2} = check_op(G, S, N, Tk, [int], '%', T1, T2),
    E1 rem E2;

%%%% (21)
eval_e(G, S, N, Tk, {{'-', _Line}, T}) ->
    case check_op(G, S, N, Tk, [int, float, fixed], '-', T) of
	F when is_record(F,fixed) ->
	    F#fixed{value = -(F#fixed.value)};
	Number ->
	    -Number
    end;
eval_e(G, S, N, Tk, {{'+', _Line}, T}) ->
    check_op(G, S, N, Tk, [int, float, fixed], '+', T);
eval_e(G, S, N, Tk, {{'~', Line}, T}) ->
    ic_error:error(G, {unsupported_op, {'~', Line}}),
    eval_e(G, S, N, Tk, T);


%% Ints are repr. by an Erlang integer val, floats and doubles by
%% Erlang floats, chars and strings must be tuplerized for type
%% checking. These tuples are removed just before returning from top
%% function.
%%
eval_e(_G, _S, _N, tk_fixed, {'<fixed_pt_literal>', _Line, X}) ->
    create_fixed(X);
eval_e(G, _S, _N, {tk_fixed, Digits, Scale}, {'<fixed_pt_literal>', Line, X})
  when Digits < 32, Digits >= Scale ->
    case convert_fixed(X, [], Digits, Digits-Scale) of
	{error, Format, Args} ->
	    ic_error:error(G, {bad_fixed, Format, Args, Line});
	FixedData ->
	    {fixed, Digits, Scale, FixedData}
    end;
eval_e(_G, _S, _N, _Tk, {'<integer_literal>', _Line, X}) -> list_to_integer(X);
eval_e(_G, _S, _N, {tk_string,_}, {'<string_literal>', _Line, X}) -> {string, X};
eval_e(_G, _S, _N, {tk_wstring,_}, {'<wstring_literal>', _Line, X}) -> {wstring, X}; %% WSTRING
eval_e(_G, _S, _N, tk_char, {'<character_literal>', _Line, X}) -> {char, hd(X)};
eval_e(_G, _S, _N, tk_wchar, {'<wcharacter_literal>', _Line, X}) -> {wchar, hd(X)}; %% WCHAR
eval_e(_G, _S, _N, _Tk, {'TRUE', _Line}) -> true;
eval_e(_G, _S, _N, _Tk, {'FALSE', _Line}) -> false;
eval_e(_G, _S, _N, _Tk, {'<floating_pt_literal>', _Line, X}) -> to_float(X);
%% Some possible error conditions
eval_e(_G, _S, _N, _Tk, {'<character_literal>', _Line, X}) -> {char, hd(X)}; %% ERROR?
%%
eval_e(G, S, N, _Tk, X) when element(1, X) == scoped_id ->
    mk_val(ictype:scoped_lookup(G, S, N, X));
eval_e(_G, _S, _N, _Tk, {default, _}) -> default;	% Default case in union
eval_e(G, _S, _N, Tk, Val) ->
    ic_error:error(G, {plain_error_string, Val, 
		       io_lib:format("value and declared type ~p differ", [Tk])}).

%% A fixed type can be 123.45 or 123 but we represent it as integers (i.e. 12345 or 123).
convert_fixed([], Acc, 0, _) ->
    list_to_integer(lists:reverse(Acc));
convert_fixed([], _Acc, _, _) ->
    {error, "Fixed type do not match the digits field", []};
convert_fixed([$.|Rest], Acc, Digits, 0) ->
    convert_fixed(Rest, Acc, Digits, -1);
convert_fixed([$.|_Rest], _Acc, _, _) ->
    {error, "Fixed decimal point placed incorrectly", []};
convert_fixed([X|Rest], Acc, Digits, Position) ->
    convert_fixed(Rest, [X|Acc], Digits-1, Position-1).


create_fixed([$0|Rest]) ->
    %% Leading zeros shall be ignored.
    create_fixed(Rest);
create_fixed(Fixed) ->
    create_fixed(Fixed, [], 0, 0, false).

create_fixed([], Acc, Total, Frac, true) ->
    {Fixed, N} = remove_trailing_zeros(Acc, 0),
    Digits = Total-N,
    Scale = Frac-N,
    #fixed{digits = Digits, scale = Scale, value = list_to_integer(Fixed)};
create_fixed([], Acc, Total, _Frac, false) ->
    %% A '.' never found. Hence, must be 2000D
    #fixed{digits = Total, scale = 0, value = list_to_integer(lists:reverse(Acc))};
create_fixed([$.|Rest], Acc, Total, _, _) ->
    create_fixed(Rest, Acc, Total, 0, true);
create_fixed([X|Rest], Acc, Total, Frac, FoundDot) ->
    create_fixed(Rest, [X|Acc], Total+1, Frac+1, FoundDot).

remove_trailing_zeros([$0|Rest], N) ->
    remove_trailing_zeros(Rest, N+1);
remove_trailing_zeros(Fixed, N) ->
    {lists:reverse(Fixed), N}.

%% Make the newly looked up value a value that can be type checked.
mk_val({_, _, {tk_string, _}, V}) -> {string, V};
mk_val({_, _, {tk_wstring, _}, V}) -> {wstring, V};  %% WSTRING
mk_val({_, _, tk_char, V}) -> {char, V};
mk_val({_, _, tk_wchar, V}) -> {wchar, V}; %% WCHAR
mk_val({_, _, enum_val, V}) -> 
    {enum_id, ic_forms:get_id2(V)};
mk_val(X) when element(1, X) == error -> X;
mk_val({_, _, _TK, V}) -> 
    V;
mk_val(V) -> V.



%% Floating point numbers
%%
%%	Conversion to Erlang floating points is neccessary because
%%	list_to_float BIF differs from IDL floats. "1e2" ".4e2" is
%%	allowed in IDL and must be translated to "1.0e2" and "0.4e2"

to_float(X) ->
    list_to_float(erlangify(X)).

erlangify([$. | R]) ->
    [$0, $. | R];
erlangify(R) ->
    look_for_dot(R).

look_for_dot([$. | R]) -> [$. | dot_pending(R)];
look_for_dot([$e | R]) -> [$., $0, $e | R];
look_for_dot([$E | R]) -> [$., $0, $E | R];
look_for_dot([X | R]) -> [X | look_for_dot(R)].

dot_pending([$e | R]) -> [$0, $e | R];
dot_pending([$E | R]) -> [$0, $E | R];
dot_pending([]) -> [$0];
dot_pending(R) -> R.


%%------------------------------------------------------------------
%%--------------- Fixed Datatype Helper Functions ------------------
%%------------------------------------------------------------------
%% Pretty?! No, but since we now the upper-limit this is the fastest way
%% to calculate 10^x
power(0) ->  1;
power(1) ->  10;
power(2) ->  100;
power(3) ->  1000;
power(4) ->  10000;
power(5) ->  100000;
power(6) ->  1000000;
power(7) ->  10000000;
power(8) ->  100000000;
power(9) ->  1000000000;
power(10) -> 10000000000;
power(11) -> 100000000000;
power(12) -> 1000000000000;
power(13) -> 10000000000000;
power(14) -> 100000000000000;
power(15) -> 1000000000000000;
power(16) -> 10000000000000000;
power(17) -> 100000000000000000;
power(18) -> 1000000000000000000;
power(19) -> 10000000000000000000;
power(20) -> 100000000000000000000;
power(21) -> 1000000000000000000000;
power(22) -> 10000000000000000000000;
power(23) -> 100000000000000000000000;
power(24) -> 1000000000000000000000000;
power(25) -> 10000000000000000000000000;
power(26) -> 100000000000000000000000000;
power(27) -> 1000000000000000000000000000;
power(28) -> 10000000000000000000000000000;
power(29) -> 100000000000000000000000000000;
power(30) -> 1000000000000000000000000000000;
power(31) -> 10000000000000000000000000000000;
power(_) ->  10000000000000000000000000000000.



%% If the result of an operation (+, -, * or /) causes overflow we use this 
%% operation. However, since these calculations are performed during compiletime,
%% shouldn't the IDL-specification be changed to not cause overflow?! But, since
%% the OMG standard allows this we must support it.
check_fixed_overflow(#fixed{digits = Digits, scale = Scale, value = Value}) ->
    case count_digits(abs(Value)) of
	overflow ->
	    {N, NewVal} = cut_overflow(0, Value),
%	    NewDigits = Digits - N,
	    if
		N > Scale ->
		    #fixed{digits = 31, scale = 0, value = NewVal};
		true ->
		    NewScale = Scale - N,
		    {NewVal2, Removed} = delete_zeros(NewVal, NewScale),
		    #fixed{digits = 31, scale = NewScale-Removed, value = NewVal2}
	    end;
	Count when Count > Digits ->
	    Diff = Count-Digits,
	    if
		Diff > Scale ->
		    #fixed{digits = Digits, scale = 0, 
			   value = (Value div power(Diff))};
		true ->
		    NewScale = Scale-Diff,
		    {NewVal, Removed} = delete_zeros((Value div power(Diff)), NewScale),
		    #fixed{digits = Digits-Removed, 
			   scale = NewScale-Removed, 
			   value = NewVal}
	    end;
	Count ->
	    {NewVal, Removed} = delete_zeros(Value, Scale),
	    #fixed{digits = Count-Removed, scale = Scale-Removed, value = NewVal}
    end.

%% This function see to that the values are of the same baase.
normalize(S, V1, S, V2) ->
    {V1, V2};
normalize(S1, V1, S2, V2) when S1 > S2 ->
    {V1, V2*power(S1-S2)};
normalize(S1, V1, S2, V2) ->
    {V1*power(S2-S1), V2}.

%% If we have access to the integer part of the fixed type we use this
%% operation to remove all trailing zeros. If we know the scale, length of
%% fraction part, we can use delete_zeros as well. But, after a division
%% it's hard to know the scale and we don't need to calcluate the integer part.
delete_zeros_value(0, N, _) ->
    {0, 32-N};
delete_zeros_value(X, N, M) when X > M, (X rem 10) == 0 ->
    delete_zeros_value((X div 10), N+1, M);
delete_zeros_value(X, N, _) ->
    {X, 32-N}.

%% If we know the exact scale of a fixed type we can use this operation to
%% remove all trailing zeros.
delete_zeros(0, _) ->
    {0,0};
delete_zeros(X, Max) ->
    delete_zeros(X, 0, Max).
delete_zeros(X, Max, Max) ->
    {X, Max};
delete_zeros(X, N, Max) when (X rem 10) == 0 ->
    delete_zeros((X div 10), N+1, Max);
delete_zeros(X, N, _) ->
    {X, N}.
                            
cut_overflow(N, X) when X > ?FIXED_MAX ->
    cut_overflow(N+1, (X div 10));
cut_overflow(N, X) ->
    {N, X}.
    
%% A fast way to check the size of a fixed data type.
count_digits(X) when X >  ?FIXED_MAX -> overflow;
count_digits(X) when X >= 1000000000000000000000000000000 -> 31;
count_digits(X) when X >= 100000000000000000000000000000 -> 30;
count_digits(X) when X >= 10000000000000000000000000000 -> 29;
count_digits(X) when X >= 1000000000000000000000000000 -> 28;
count_digits(X) when X >= 100000000000000000000000000 -> 27;
count_digits(X) when X >= 10000000000000000000000000 -> 26;
count_digits(X) when X >= 1000000000000000000000000 -> 25;
count_digits(X) when X >= 100000000000000000000000 -> 24;
count_digits(X) when X >= 10000000000000000000000 -> 23;
count_digits(X) when X >= 1000000000000000000000 -> 22;
count_digits(X) when X >= 100000000000000000000 -> 21;
count_digits(X) when X >= 10000000000000000000 -> 20;
count_digits(X) when X >= 1000000000000000000 -> 19;
count_digits(X) when X >= 100000000000000000 -> 18;
count_digits(X) when X >= 10000000000000000 -> 17;
count_digits(X) when X >= 1000000000000000 -> 16;
count_digits(X) when X >= 100000000000000 -> 15;
count_digits(X) when X >= 10000000000000 -> 14;
count_digits(X) when X >= 1000000000000 -> 13;
count_digits(X) when X >= 100000000000 -> 12;
count_digits(X) when X >= 10000000000 -> 11;
count_digits(X) when X >= 1000000000 -> 10;
count_digits(X) when X >= 100000000 -> 9;
count_digits(X) when X >= 10000000 -> 8;
count_digits(X) when X >= 1000000 -> 7;
count_digits(X) when X >= 100000 -> 6;
count_digits(X) when X >= 10000 -> 5;
count_digits(X) when X >= 1000 -> 4;
count_digits(X) when X >= 100 -> 3;
count_digits(X) when X >= 10 -> 2;
count_digits(_X) -> 1.
    
%%------------------------------------------------------------------
%%--------------- END Fixed Datatype Helper Functions --------------
%%------------------------------------------------------------------